Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.

Tuesday, February 1, 2022

Supernothing

The things that keeps astrophysicists up at night are the irritating little questions about the universe that are simple to ask, and wildly difficult to answer.

Of course, they probably like being kept up at night.  Part of the job, really.

In any case, one of the most curious is why the universe is almost isotropic, but not quite.  "Isotropic" means, basically, "the same everywhere you look."  You can pick out any point in the night sky, and the amount of matter and energy within that region should be the same as if you picked out somewhere else.  Now, there are local conglomerations of matter -- you're residing on one, and working your way up the size ladder, the Solar System and the Milky Way are both clumps with higher matter density than the surrounding regions -- but on the largest scales, you'd expect things to be evenly spread out.

When I first ran into the idea of the Big Bang as a teenager, this was one of the hardest things for me to grasp.  If there really was a giant explosion at the beginning of the universe, why can't we find out where that explosion occurred?  You'd expect high matter density in that direction, and low density at the antipodal spot in the sky.  In fact, you see no such thing.  But far from being an argument against the Big Bang, it's an argument in its favor.  I didn't understand why until I took an astronomy class in college, and the professor, Dr. Whitmire, explained it as follows:

Imagine you're on the surface of an enormous balloon, and the surface is covered with dots.  You're standing on one of the dots.  Then, someone inflates the balloon.  What do you see?  You see all the other dots moving away from you, and in every direction, there are just about equal numbers of dots.  It's isotropic -- similar densities and recession speeds no matter where you look.  It doesn't depend on your perspective; you didn't just happen to choose the one dot that was at the center of the expansion.  It would look the same if you were standing on any other dot.  The reason is that the dots aren't moving through space; the space itself -- the surface of the balloon -- is expanding, carrying the dots with it.

"So there is no center of the universe," Dr. Whitmire said.  "Or everywhere is the center.  It amounts to the same thing."

In the first milliseconds after the Big Bang, the expansion rate was so fast that it smoothed everything out, spreading matter and energy fairly uniformly (again, allowing for localized clumps to form, but even the clumps would be expected to have a uniform distribution, like chocolate chips in cookie dough).  When the cosmic microwave background radiation was discovered in 1965 by Arno Penzias and Robert Wilson, it was powerful evidence for the Big Bang Model, especially when they found that -- like matter -- the CMBR was isotropic: the same no matter where you looked.

Well, almost.  One of the annoying little questions I mentioned in the first paragraph is that the CMBR is nearly isotropic -- but there are "cold spots," which have a lower temperature than the surrounding regions.  I'm not talking about a big difference, here; the average temperature in interstellar space is 2.7 K (-270.5 C), and the largest of these cold spots -- the Eridanus Supervoid -- is 0.00007 K lower.  The difference was small enough that at first it was thought to  be a glitch in the equipment or some sort of error in the data, but repeated measurements by the Wilkinson Microwave Anisotropy Probe (WMAP) has found that it is, in fact, a real phenomenon.

[Image licensed under the Creative Commons Piquito veloz, Eridanus supervoid in celestial sphere, CC BY-SA 4.0]

The "Eridanus Supervoid" is a name for the universe's largest collection of nothing.  It's a region on the order of between 500 million and one billion light years in diameter, in which there is so little matter that if the Earth sat in the center of it, you wouldn't be able to see a single star in the night sky.  It wouldn't have been until the 1960s that we would have found out about the existence of stars and galaxies, at the point that there were telescopes powerful enough to see something that distant.

This empty spot is a bit of a bother to cosmologists.  During the "inflationary period" -- thought to be between 10 ^-36 and 10 ^-33 seconds after the Big Bang -- space was stretching so unimaginably fast that it smoothed out most of the local variability, rather like taking a crumpled-up bedsheet and having four people pull on the corners; most of the wrinkles and folds disappear.

So what caused the Eridanus Supervoid?  Are we left with, "Well, it just happened because it happened?"

A new study hasn't exactly answered the question, but has generated another piece of data -- and a partial explanation.  A paper in Monthly Notices of the Royal Astronomical Society describes research that uses information from WMAP and from the Dark Energy Survey to see what's different about that region of space, and they found something curious.  The mysterious and elusive "dark matter" -- a component of the universe that amounts to 27% of its detectable mass, and six times more than all the ordinary matter put together -- has as its sole observable characteristic its gravitational effects on the matter and space around it, and that's measurable even if you can't see it, because it bends the path of light passing through it.  (The "gravitational lensing effect.")  And the recent study found that the Eridanus Supervoid has way less dark matter than is normal for other regions in the universe.  As it expands, it becomes a sink for energy -- a photon crossing it is moving through successively more stretched-out space, and its energy drops, as does its frequency.  The photon, therefore, is red-shifted, not because its source is moving away from us, but because it's traveling through expanding space.

As study co-author Juan Garcia-Bellido, of the Institute for Theoretical Physics at the University of Madrid, explained:

Photons or particles of light enter into a void at a time before the void starts deepening, and leave after the void has become deeper.  This process means that there is a net energy loss in that journey; that’s called the Integrated Sachs-Wolfe effect.  When photons fall into a potential well, they gain energy, and when they come out of a potential well, they lose energy.  This is the gravitational redshift effect.

Then once the region became a little less dense than the surrounding areas, every photon that crossed through it dropped its temperature and energy density a little more.

This still doesn't explain where the original anisotropy came from; the current thought is that it was caused by random fluctuations on the quantum level when the universe was still smaller than a grain of sand.  At that scale and energy, quantum effects loom large, and any minor unevenness might get "locked in" to the pattern of the universe; after that the process described by Garcia-Bellido takes over and makes it bigger.

And 13.7 billion years later, we have a huge blob of space that is just about completely empty, and ridiculously cold.  The Eridanus Supernothing.

So that's our excursion into deep space for the day.  And some more data on one of those mysterious questions that have, thus far, defied all attempts to answer them.  I'm nowhere near an expert, but I'm still endlessly fascinated with these sorts of things -- even if all we've got at the moment are unsatisfying partial solutions.

*******************************

It's obvious to regular readers of Skeptophilia that I'm fascinated with geology and paleontology.  That's why this week's book-of-the-week is brand new: Thomas Halliday's Otherlands: A Journey Through Extinct Worlds.

Halliday takes us to sixteen different bygone worlds -- each one represented by a fossil site, from our ancestral australopithecenes in what is now Tanzania to the Precambrian Ediacaran seas, filled with animals that are nothing short of bizarre.  (One, in fact, is so weird-looking it was christened Hallucigenia.)  Halliday doesn't just tell us about the fossils, though; he recreates in words what the place would have looked like back when those animals and plants were alive, giving a rich perspective on just how much the Earth has changed over its history -- and how fragile the web of life is.

It's a beautiful and eye-opening book -- if you love thinking about prehistory, you need a copy of Otherlands.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]


Monday, January 31, 2022

A spoon full of embarrassment

Of all the unpleasant feelings in the world, I think I hate humiliation the most.

I once said that I would rather be physically beaten than humiliated.  I can't even handle watching when other people embarrass themselves, which is why I kind of hate most sitcoms.  I mean, sometimes it can be undeniably funny, like my friend's experience at a restaurant:
Server:  What would you like?
My friend:  I'd like the fried chicken half, please.
Server:  What side?
My friend (uncertainly):  Um, I don't know... Left, I guess.
Server:
My friend:
Server:  Ma'am, I meant which side order would you like with your dinner.
My friend: *resolves never to set foot in that restaurant again*
But even in situations like that, I totally understand my friend's reaction of never wanting to see that server again.  In her place, I'd be absolutely certain that the server would see me across the street or something, and elbow her friends and say, "Hey, look!  It's left chicken guy!"

So I can barely even imagine what it must be like to humiliate yourself while being watched by millions.  This is what happened in 1973 to self-proclaimed psychic Uri Geller, who was invited to demonstrate his supposed abilities on the Johnny Carson Show.  Before his TV career, Carson had been a professional stage magician, so he knew how easy it is to fool people -- and he knew all the tricks a faker would use to hoodwink his audience.

Uri Geller in 2009 [Image licensed under the Creative Commons Dmitry Rozhkov, Uri Geller in Russia2, CC BY-SA 3.0]

He set Geller up with props like the ones he used in his "psychic demonstrations" -- and wouldn't let Geller use his own props, nor handle the ones Carson provided before the show.  The result was twenty minutes of the most cringeworthy television I've ever seen, as Geller failed over and over, blaming whatever he could think of -- Carson's disbelief, the hostile atmosphere, the response of the audience.  He finally settled on "I'm not feeling strong tonight."

Here's a clip of the incident, if you can stand to watch it.

Every time I think of Geller, I always am baffled by why this single experience didn't lead him to vanish entirely.  If something like that happened to me, I'd probably change my name and consider plastic surgery.  But no -- after a brief time when he seemed set back by his catastrophic performance with Carson, he bounced back and became more popular than ever.

So this is two things I don't get, combined into one; how Geller didn't retreat in disarray, and how anyone continued to believe that what he does is anything more than a clever magic trick.  But neither happened.  In fact, the reason this comes up today is because a friend and loyal reader of Skeptophilia sent me a link that Geller is still at it, almost fifty years later, this time with a pronouncement warning NASA to get ready, because we're going to have an alien invasion soon.

The most amusing part of it is the reason he thinks we're due for ET to land; the discovery of a peculiar radio source that pulsates -- but (compared to other pulsating radio sources) with a verrrrrry long period.  This source flashes on and off every twenty minutes; a more ordinary pulsar flashes on twenty times a second.  So far, astronomers are still trying to figure out a natural phenomenon that could cause this really slow pulsation rate, but at present all they have are guesses.

But here's the funny part, apropos of Geller; he claims that this radio source is the signal that the aliens are about to land.  Unfortunately, this runs head-first into the fact that the anomalous astronomical object is four thousand light years away.  Which means that if the aliens were sending that signal toward Earth, it was intended for the Sumerians.

Be that as it may, Geller said we better get ready.  "A team mapping radio waves in the universe has discovered something unusual that releases a giant burst of energy three times an hour and it’s unlike anything astronomers have seen before," Geller posted on Instagram.  "No doubt in my mind that this is connected to alien intelligence way way superior than ours.  Start deciphering their messages!  They are preparing us for a mass landing soon!  #nasa #hoova #spectra #spectra #aliens."

I'm curious about what he thinks we should ready ourselves.  I mean, what's he personally going to do to save humanity from the aliens?  Bend a spoon at them?

Anyhow, I guess not everyone overreacts to being humiliated the way I do.  Probably a good thing, that; one of my many faults is taking myself way too seriously.  But really.  How does Geller do it?  To me that's more impressive than any of his alleged psychic talents.  He should bill himself as The Amazing Impervious Man, or something.

*******************************

It's obvious to regular readers of Skeptophilia that I'm fascinated with geology and paleontology.  That's why this week's book-of-the-week is brand new: Thomas Halliday's Otherlands: A Journey Through Extinct Worlds.

Halliday takes us to sixteen different bygone worlds -- each one represented by a fossil site, from our ancestral australopithecenes in what is now Tanzania to the Precambrian Ediacaran seas, filled with animals that are nothing short of bizarre.  (One, in fact, is so weird-looking it was christened Hallucigenia.)  Halliday doesn't just tell us about the fossils, though; he recreates in words what the place would have looked like back when those animals and plants were alive, giving a rich perspective on just how much the Earth has changed over its history -- and how fragile the web of life is.

It's a beautiful and eye-opening book -- if you love thinking about prehistory, you need a copy of Otherlands.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]


Saturday, January 29, 2022

Locking the echo chamber

It must be awfully convenient to start out from the baseline assumption that everyone who disagrees with you is wrong.

This observation comes about because Thursday was International Holocaust Remembrance Day, and I posted the following on Facebook: "On this Holocaust Remembrance Day, I'm thinking about our cousins, Armand Simon, Céline (Bollack) Simon, and Irène Simon, and Baila Dvora (Bloomgarden) Serejski, Avish Serejski, Tsipe Serejski, and Sholem Serejski, who died at the hands of the Nazis in Auschwitz.  May they never be forgotten."  I also appended a link to a post I did five years ago about the Simon family, who were part of the French Resistance.

Most of the responses were wonderful, but one person, a cousin of mine, wrote the following:

I could never understand how everyday people went along with packing their possessions up and moving to the ghetto thinking how could it get worse?  And yet it became much worse.  I see this going on in our country today.  When we visited Hawaii last March to see our daughter who was living there, we had to get a specific COVID test to enter the state.  And it was negative.  But when we got there, it wasn’t from the lab approved by their Governor and we were hauled into an area for “processing”.  They called our hotel and we’re going to force us in a 14 day quarantine - they wouldn’t even look at our antigen test results!  And we went to a lab at the airport recommended by our airline.  Well I refused to pay for a resort and be forced to stay in a hotel room for 14 days, so we told them we would stay at our daughter’s apartment.  I wasn’t about to give this state a penny of our money and be under their control.  When I said to the lady at the airport Aloha, Welcome to Hawaii - she replied, "We don’t want you here."  I felt like we were no longer in the USA.  And you should see all the homeless in Hawaii because the Governor there shut down all the businesses - tents everywhere. For a state that relies on tourism as a huge part of their livelihood- this was beyond stupid.  Many people in the tourist industry had to move to the mainland and those that couldn’t afford to, now had to live on the streets.  And now you can’t go in restaurants or bars unless you have a vaccine passport.  I have a bad reaction to vaccines so I’m not about to get that shot and it’s my body - nobody should be forced to have to take an injection - EVER!  Our country is FUBAR.  Thank God we live in Florida and our Governor is the best combination of intelligence and common sense.  To think I have to check which states I can travel to is unconscionable.  Our country is on a very bad path as a whole. We can only hope that at some point there will be a mass resistance.

When someone pointed out that it was out of line to compare being mildly inconvenienced on your Hawaii vacation to six million people being systematically killed by the Nazis, she responded:

My point was definitely not a comparison. My point is that we are like the frog and boiling water theory if we don’t pay attention to our gradual loss of freedoms. And that is exactly what is taking [sic] with President Numbnuts in office right now.

And damn straight I am in the right state. I would appreciate if all the people flocking here from Democrat states would stay the hell out unless they have the intelligence to know why they want to be here. Don’t come here and ruin our freedom!

This, of course, isn't the first thing like this she's posted; it's just the first one directed at me.  She's had gems like a diatribe starting out "All Democrats are pinheads," implying that one-half of the American public are hopelessly stupid.  No need to know anything else about them; Democrat = idiot.  Done thinking.

I honestly can't comprehend this level of confident arrogance.  One of my (many) besetting sins is that I'm almost never 100% sure of anything; to me, most of the world is made up of gray areas, ambiguity, and extenuating circumstances.  But my cousin's attitude goes way beyond being sure of oneself.  Confidence and a strong trust in your own beliefs and principles are just fine; in her, it has morphed into a conviction that the people who share her beliefs are the only ones worth listening to.  

It's a scary position to be in.  I wrote a couple of years ago about how absolutely essential it is to keep in mind that your opinion could be based in error -- and cited some research showing that this willingness to consider our own fallibility is essential in science.  (I'd argue that it's essential in damn near everything.)

It reminds me of what Kathryn Schulz said, in her amazing TED Talk "On Being Wrong:"

It's like we want to believe that our minds are these perfectly transparent windows, and we just gaze out of them and describe the world as it unfolds.  And we want everybody to gaze out of the exact same window and see the exact same thing...  If you want to rediscover wonder, you have to step outside of that tiny, terrified space of rightness -- and look around at each other, and look at the vastness and complexity and mystery of the universe, and be able to say, "Wow.  I don't know.  Maybe I'm wrong."

I chose not to try to argue with her.  Maybe that was the cowardly choice, but my impression is that it would have been entirely futile.  Once you've landed in that position -- believing that everyone who disagrees with you is either misinformed, stupid, or lying outright -- you're kind of stuck there.  I don't shy away from an argument when there's ground to be gained, or at least when both sides are listening; but this person has so locked herself in an echo chamber that it's pointless even to engage.

If what I really crave is slamming my head into a wall, it'd be easier and quicker just to go find a wall and do it.

[Image licensed under the Creative Commons Evbestie, FilterBubble, CC BY-SA 4.0]

In any case, I just decided to disconnect.  I'm kind of done posting on social media.  I'll still throw links to Skeptophilia on Facebook and Twitter every day, and probably will continue to post the occasional pic of my dogs on Instagram, but other than that, I've kind of had it.  I'm just weary unto death of the vitriol -- when you can't post a tribute to relatives who died in the Holocaust without it turning into a Fox News-inspired extremist screed, it's a sign that the platform itself is no longer worth the time and anguish.  And I unfriended my cousin (reducing the number of my blood relatives who still want to have anything to do with me to "almost one"), because I know about her that one of her mottos is "Death before backing down."  Interacting with someone like that isn't worth the toll it takes on me personally.

What that says about the state of affairs in the United States today is scary, though.  The media found out a couple of decades ago that polarization and agitation gets viewers, and has whipped up the partisan rancor to the point that each side thinks the other is actively evil.  It's kind of ironic that the whole nasty exchange started because of a post about the Holocaust, though.  It reminds me of the trenchant quote -- attributed incorrectly to Werner Herzog, and actually of unknown provenance -- "Dear America, you are waking up, as Germany once did, to the awareness that one-third of your people would happily kill another one-third, while the remaining one-third stands there watching."

*************************************

It's kind of sad that there are so many math-phobes in the world, because at its basis, there is something compelling and fascinating about the world of numbers.  Humans have been driven to quantify things for millennia -- probably beginning with the understandable desire to count goods and belongings -- but it very quickly became a source of curiosity to find out why numbers work as they do.

The history of mathematics and its impact on humanity is the subject of the brilliant book The Art of More: How Mathematics Created Civilization by Michael Brooks.  In it he looks at how our ancestors' discovery of how to measure and enumerate the world grew into a field of study that unlocked hidden realms of science -- leading Galileo to comment, with some awe, that "Mathematics is the language with which God wrote the universe."  Brooks's deft handling of this difficult and intimidating subject makes it uniquely accessible to the layperson -- so don't let your past experiences in math class dissuade you from reading this wonderful and eye-opening book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]



Friday, January 28, 2022

Bad Blood

The moral of this short story is either "Don't judge a book by its cover" or "Be careful who you piss off."  Both of them seem like decent takeaways.

***************************************

Bad Blood

Melba Crane looked up as Dr. Carlisle entered the room.  She smiled, revealing a row of straight, white, and undoubtedly false teeth.  “Hello, doctor!  I don’t think we’ve met yet.  How are you today?”

Dorian Carlisle looked at his new patient.  She was tiny, frail-looking, with carefully-styled curly hair of a pure snowy white, and eyes the color of faded cornflowers.  “I’m fine, Mrs. Crane.  I’m Dr. Carlisle—I’m looking after Dr. Kelly’s patients while he’s on vacation.”

Mrs. Crane nodded, and raised one thin eyebrow.  “My, you look so young.  It’s hard to believe you’re a doctor.”  She giggled.  “I’m sorry, that was rude of me.”

“Not at all.”  Dr. Carlisle lifted one of Mrs. Crane’s delicate wrists and felt gently for a pulse.  “I take it as a compliment.”

“It will be even more of a compliment when you’re my age.  I just turned eighty-seven three weeks ago.”

“Well, happy belated birthday.  I hear you had kind of a rough night last night.”

Mrs. Crane gave a little tsk and a dismissive gesture of her hand.  “Just a few palpitations, that’s all.  Nothing this old heart of mine hasn’t seen a hundred times before.”

“Still, let’s give a listen.”  Dr. Carlisle pressed his stethoscope to her chest.  Other than a slight heart murmur, the beat sounded steady and strong—remarkable for someone her age.

“How long will Dr. Kelly be away?”  Mrs. Crane asked, as Dr. Carlisle continued his examination.

“Two weeks.  He and his family went to Hawaii.”

“Oh, Hawaii, how lovely.  Such a nice man, and with a beautiful wife and two wonderful children.  He’s shown me pictures.”

Dr. Carlisle nodded.  “They’re nice folks.”  He pointed to a small framed photograph of a somewhat younger Mrs. Crane with a tall, well-built man, who appeared to be about thirty.  The man was darkly good looking, with a short, clipped beard and angular features.  He wore a confident smile, and stood behind Mrs. Crane, who was seated, her legs primly crossed at the ankle.  The man had his hand on her shoulder.

“Your son?” Dr. Carlisle asked.

Mrs. Crane nodded, and smiled fondly.  “Yes, that’s Derek.  My only son.”

“Do you get to see him often?”

“Oh, yes.  He visits me every day, especially now that I’m here in the nursing home.”  She paused and sighed.  “His father was Satan, you know.”

Dr. Carlisle froze, and he just stared at her.  She didn’t react, just maintained her gentle smile, her blue eyes regarding him with grandmotherly fondness.

He must have misheard her.  What did she say?  His father was a saint.  His father liked satin.  His father was named Stan.  His father looked like Santa.  But each of those collided with his memory, which stubbornly clung to what it had first heard.  Finally, he said, “I beg your pardon?”

“Satan,” Mrs. Crane said, her expression still mild and bland.  “That’s Derek’s father.  Lucifer.  He used to visit, too, quite often, when Derek was little, but I expect he has other concerns these days.”  She giggled again.  “And I’m sure he’s had dalliances with other ladies since my time.  Quite a charmer, you know, whatever else you might say about him.”

“Oh,” Dr. Carlisle croaked out.  “That’s interesting.”

“Well, of course, you couldn’t ask him to be faithful.”  If she heard his tentative tone, she gave no sign of it.  “He isn’t that type.  I did have to put up with a great deal of disapproval from people who thought it was immoral that I had a child out of wedlock.  But after all—” she tittered—“what else could they have expected?  He’s Satan, after all.”

"Satan," from Gustave Doré's illustrations for Milton's Paradise Lost (1866) [Image is in the Public Domain]

Dr. Carlisle cleared his throat.  “Yes, well, Mrs. Crane, I have to finish my examination of you, and see a couple of other patients this morning, so…”  He trailed off.

Mrs. Crane gave her little wave of the hand again.  “Oh, of course, doctor.  I’m being a garrulous old woman, going on like that.  I’m sorry I’ve kept you.”

“It’s no problem, really.  And I wouldn’t worry about the palpitations—usually they’re not an indication of anything serious, especially if they don’t last long, as in your case.  Your blood pressure is fine, and your last blood work was normal, so I don’t think you have anything to worry about.”

“I tried to tell the nurse that.  But she insisted that I see the doctor this morning.  I’m sorry I’m keeping you away from patients who need your help more than I do.”

“No worries, Mrs. Crane.”  Dr. Carlisle hung his stethoscope around his neck.  “Take care, and have a nice day.”

“You too, doctor.  It’s been lovely talking to you.”

Dr. Carlisle opened the door, and exited into the hall, feeling a bit dazed.

He stood for a moment, frowning slightly, and then came to a decision.  He walked off down the hall toward the nurses’ station, and set his clipboard on the counter, and leaned against it.

“Excuse me, nurse…?”  He smiled.  “I’m covering for Dr. Kelly this week and next.  I’m Dr. Carlisle—my office is up at Colville General.”

The nurse, a slim, middle-aged woman with gold-rimmed glasses and short salt-and-pepper hair, gave him a hand.  “I’m glad to meet you.  Dana Treadwell.  If there’s anything I can do…”

“Well, actually,” Dr. Carlisle said,  “I do have a question.  About Mrs. Crane, in 214.”

Dana gave him a quirky half-smile.  “She’s an interesting case.”

Dr. Carlisle nodded.  “That’s my impression.  She’s here because of advanced osteoporosis, but is there anything else that you can tell me that might be helpful?”

“Has periodic mild cardiac arrhythmia.  She had a full cardio workup about six months ago, showed nothing serious of note.  Some tendency to elevated blood pressure, but nothing that medication can’t keep in check.”  She paused, gave Dr. Carlisle a speculative look.  “Some signs of mild dementia.”

“That’s what I wanted to ask you about.  Is she… is she delusional?”

“That depends on what you mean,” Dana said.  “Mentally, I hope I’m as with it when I’m eighty-seven.  But she is prone to… flights of fancy.  Particularly about her past.”

Dr. Carlisle didn’t answer for a moment.  Should he mention the whole Satan thing?  He decided against it.  “She does seem to like telling stories,” he finally said.

Dana's smile turned into a full-fledged grin.  “That she does.”

***

The following day, Dr. Carlisle was making his rounds, and passed Mrs. Crane’s room, and heard a male voice.  Curiosity did battle with reluctance to talk to her again, and curiosity won.  He knocked lightly, then stepped into the room.

Mrs. Crane looked up from a conversation she was having with a man who was seated at the edge of the bed, gently holding her hand.  When the man turned toward him, Dr. Carlisle immediately recognized him as the man in the photograph—noticeably older, perhaps in his mid to late fifties, but clearly the same person.  He still had the same carefully-maintained short beard, the same dark handsomeness, the same sense of strength, energy, presence.

“Oh, doctor, I’m so glad you’ve stopped by!” Mrs. Crane said.  “This is my son, Derek.”

“Dorian Carlisle,” Dr. Carlisle said.  “Nice to meet you.  I’m going to be your mother’s doctor for the next two weeks, until Dr. Kelly returns.”

Derek got up and extended a hand.  “Derek Crane."  They clasped hands.  Derek’s hand jerked, and a quick flinch crossed his face.

“Sorry,” Dr. Carlisle said, almost reflexively.

“It’s nothing.  Three weeks ago, I hurt my hand doing some home renovations.  I guess it’s still not completely healed.”

“I didn’t mean to…” Dr. Carlisle started, but Derek cut him off.

“It’s nothing.  Mom has been telling me about your visit yesterday.  It sounds like she talked your ear off.”

Dr. Carlisle smiled.  “Not at all. It was a pleasure.  I’d much rather chat with my patients and get to know them—otherwise, all too easily this job starts being about symptoms and treatments, and stops being about people.”

Mrs. Crane beamed at them.  “Well, it’s so nice of you to take time from your busy schedule to stop in.  I haven’t had any more palpitations.”

“That’s good,” Dr. Carlisle said.  “I just wanted to see how you were doing.  Nice to meet you, Derek.”

“Likewise.” Derek smiled.

Was there something—tense? speculative? about the smile?

No, that was ridiculous.  Mrs. Crane had just primed him to be wary of her son because she’s delusional.

Dr. Carlisle exited the room, and then stopped suddenly, his face registering shock.  He looked down at his hands.  On his right ring finger he wore his high school class ring, from St. Thomas More Catholic Academy.  He raised the ring to his eye, and saw, on each side of the blue stone in the setting, a tiny engraved cross.

***

That night, Dr. Carlisle told his girlfriend about Mrs. Crane over dinner.

“Now I want to meet this lady.”  Nicole grinned.

“Can’t do that. I can’t even tell you her name.  Privacy laws, and all that. I probably shouldn’t have even told you as much as I did.”

“It’s not like I’m going to go and tell anyone.  And I want to hear about your job.  It’s a huge part of your life.”

He took a sip of wine.  “And this one was just so out of left field.  I’ve dealt with people with dementia before, but they always show some kind of across-the-board disturbance in their behavior.  This was like, one thing.  In other respects, she seems so normal.”

“You didn’t talk to her that long.”

“No,” he admitted.  “But you learn to recognize dementia when you see it.  There was something about the way she looked at you—you could tell that her brain was just fine.”

Nicole raised an eyebrow.  “So, you think she really did have a fling with Satan?”

He scowled.  “No, of course not.  But I think she believes it.  But then…” he trailed off.

“But then what?”

“Her son jumped when I shook his hand, like he’d been shocked, or something.  Then he made some excuse about how he’d hurt his hand a couple of weeks ago.  But I noticed afterwards—I was wearing my high school ring.  It’s got crosses engraved on it.  And it was probably blessed by the bishop.”

“You’re kidding me, right?  I thought you’d given up all of that religious stuff when you moved out of your parents’ house.”

“I did.”

“Maybe you didn’t,” Nicole said.

“All I’m saying is that it was weird.”

“You’re acting pretty weird, yourself.”

“I just wonder if it might not be possible to test it.  See if maybe she’s telling the truth.”

“You do believe her!  Dorian, you’re losing it.  Satan?  You think she got laid by Satan?”

He sat back in his chair.  “I dunno,” he finally said.  “All I can say is, she believes it enough that it made me wonder.”

***

The next day, other than a quick walk down the hall in the early morning hours, Dr. Carlisle avoided that wing of the nursing home until after lunch.  When he finally went down the hallway toward room 214, he found that his heart was pounding.  But he was stopped in the hall before he got to Mrs. Crane’s room by the nurse he’d spoken to two days earlier, Dana Treadwell.

“You missed some excitement,” Dana said.

“What happened?”

“A bad spill.  Broken leg, possible fractured pelvis.”

Dr. Carlisle swallowed.  “Which one of the patients?”

“Not a patient,” Dana said.  “Mrs. Crane’s son.  Slipped on wet tile right outside his mother’s room, and fell.  Hard to believe you could be so badly hurt from a fall.  They brought him to Colville General—I heard he’s still in surgery.”

“That’s too bad,” he said, trying to keep his voice level.

“Mrs. Crane was really upset.”

“I’m sure,” Dr. Carlisle said.

Dana seemed to pick up the odd tone in his voice.  She raised one eyebrow.  “Yeah.  She was completely distraught.”

“Really?”

Dana nodded.  “Especially after her ex-husband came by.  We finally had to give her a sedative.”

Dr. Carlisle tried to think of something to say, and finally just choked out, “That’s too bad,” and turned away, hoping that Dana wouldn’t notice the ghastly expression on his face.  He stuck his hand in his lab jacket pocket, and fingered the small glass bottle, now empty, that he’d filled early that morning at the font in the nursing home’s chapel.

“Oh, and Dr. Carlisle?” Dana said, and he turned.

“You might want to know that before we finally got her to go to sleep, your name came up.”

“Me?” Dr. Carlisle squeaked.  “What did she say?”

“Something about your ‘needing an ocean of holy water.’  You might want to let Dr. Bennett handle her case from now on.”  She smiled.  “Just a suggestion.”

*************************************

It's kind of sad that there are so many math-phobes in the world, because at its basis, there is something compelling and fascinating about the world of numbers.  Humans have been driven to quantify things for millennia -- probably beginning with the understandable desire to count goods and belongings -- but it very quickly became a source of curiosity to find out why numbers work as they do.

The history of mathematics and its impact on humanity is the subject of the brilliant book The Art of More: How Mathematics Created Civilization by Michael Brooks.  In it he looks at how our ancestors' discovery of how to measure and enumerate the world grew into a field of study that unlocked hidden realms of science -- leading Galileo to comment, with some awe, that "Mathematics is the language with which God wrote the universe."  Brooks's deft handling of this difficult and intimidating subject makes it uniquely accessible to the layperson -- so don't let your past experiences in math class dissuade you from reading this wonderful and eye-opening book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]



Thursday, January 27, 2022

Drinking scepters

I mean no disrespect to archaeologists, but there's a fundamental difficulty with trying to understand a vanished culture when all you have is fragmentary remains; too often, there's just insufficient evidence to be certain if you're doing more than guessing.

This was one of the main points of the classic essay "Body Ritual Among the Nacirema," by Horace Miner, which appeared in American Anthropologist in 1956.  Miner was riffing on the determination of anthropologists to analyze everything as if it were part of some kind of tribal religious artifact, so applied those same biases to things commonly found in American bathrooms -- mirrors, sinks, bottles of shampoo, combs and brushes, and so on.  The essay is hilarious but at the same time neatly poniards the tendency to interpret, and very likely misinterpret, the significance of objects left behind by cultures we know little about.

The topic comes up because of a paper out of Cambridge University that appeared in Antiquity last week.  It concerned a set of gold and silver tubes that had been dug up at the Maikop kurgan (grave mound), in the Caucasus Mountains of southern Russia, way back in 1897.  The tubes were decorated with intricate carvings; several had ornaments shaped like bulls or oxen. 

Details of some of the Maikop tubes

The beauty of the decoration, and the fact that they were fashioned from precious metals, led to their being called "scepters."  This automatically conjured up images of use as symbols of authority by royalty, or instruments for invoking spirits (think "magic wands") by priests.  Some, more prosaically, thought they might form the struts supporting a canopy, once again for someone of high prestige.

Over a century later, the artifacts were re-examined, including a microscopic analysis of residue found inside the tubes.  This residue had a couple of odd components; grains of barley starch and cereal phytoliths (mineral crystals found inside plant seeds).  The interior of the end of the tube was shaped in such a way that it would have accommodated a conical piece of plant stem, particularly a piece of cut reed (Phragmites) that could have acted as a filter.  The conclusion?

The researchers believe that the "scepters" were actually straws for drinking beer.

Now, in favor of their use by (or in honor of) a prestigious person, there are admittedly the facts that (1) the straws were made of gold and silver, and (2) they ended up in the grave at Maikop.  The surmise is that they were probably made for, and used at, the funeral of the person buried in the kurgan, and the beer drinking wasn't just to get a buzz, but was part of the ritual.  But we're not talking insignificant amounts, here.  The authors write:

[A] single, early second-millennium BC burial in Tell Bagüz near Mari in eastern Syria, containing eight bronze tip-strainers, appears to support our hypothesis.  The set of eight drinking tubes in the Maikop tomb may therefore represent the feasting equipment for eight individuals, who could have sat to drink beer from the single, large jar found in the tomb.  The volume of this vessel (32 litres) suggests that each participant's share would be about four litres (or seven pints) per person.

Okay, I'm admittedly a lightweight -- two pints is my limit -- but seven?  Even considering that it's likely our modern brewing techniques result in a beer with higher alcohol content, that is a lot of beer to drink at one go.  I can see the funeral going as follows:

Priest:  Dearly beloved, we are gathered here to pay our respects to our departed brother... um... hang on.  *runs outside to take a piss*  *returns*  Okay, where was I?  Oh, yeah... our departed brother, who left this life only a day ago...

Participant 1:  Hold on a second.  *runs outside to take a piss*  *returns*  Thanks, do go on.

Priest:  ... only a day ago, and was sadly gathered unto the arms of...

Participant 2:  Sorry.  *runs outside to take a piss*  *returns*  All right, what were you saying?

Priest (annoyed):  Anyone else, before I go on?

*five more people run outside to take a piss*

Be that as it may, the current analysis is pretty interesting, and it sounds like their hypothesis is supported by some decent evidence, but I do still think you have to be cautious not to over-conclude.  Trying to piece together a culture based on (extremely) fragmentary evidence is a sketchy enterprise.  Once again, I'm not meaning to diss the archaeologists, here; they do fantastic, and fascinating, work, and it's better to at least have a guess about the purpose of an artifact than simply to shrug our shoulders.

But it always makes me think about what archaeologists five thousand years from now will make of the artifacts left behind by us.  Think about it; trying to infer modern culture from the cover of a barbecue grill, a car tire, a piece of a mug saying "I 💙Cancun," a bird feeder, and a flip-flop.  Considering how far off the mark you could go with those makes misinterpreting beer straws as royal scepters seem like kind of a near miss.

*************************************

It's kind of sad that there are so many math-phobes in the world, because at its basis, there is something compelling and fascinating about the world of numbers.  Humans have been driven to quantify things for millennia -- probably beginning with the understandable desire to count goods and belongings -- but it very quickly became a source of curiosity to find out why numbers work as they do.

The history of mathematics and its impact on humanity is the subject of the brilliant book The Art of More: How Mathematics Created Civilization by Michael Brooks.  In it he looks at how our ancestors' discovery of how to measure and enumerate the world grew into a field of study that unlocked hidden realms of science -- leading Galileo to comment, with some awe, that "Mathematics is the language with which God wrote the universe."  Brooks's deft handling of this difficult and intimidating subject makes it uniquely accessible to the layperson -- so don't let your past experiences in math class dissuade you from reading this wonderful and eye-opening book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]



Wednesday, January 26, 2022

The spirits speak

A friend and loyal reader of Skeptophilia sent me a link to a post that appeared a couple of weeks ago over at the blog Future and Cosmos with the message, "I'm honestly curious to hear what you think of this."

The post had to do with a series of experiments done by a French researcher, Paul Joire, back in the first two decades of the twentieth century.  Joire is an interesting fellow; he was fascinated with claims of the paranormal, but much like the British-based Society for Psychical Research, did his level best to approach things from a scientific standpoint.  That's not to say he didn't have some significant missteps, though.  He invented a device he called a "sthenometer" which he said could detect the presence and configuration of the "nervous force" emitted by the human body, and suggested that it could potentially be used for diagnosis of illness -- but later experiments found that all it was picking up on was body heat.

Paul Joire, ca. 1910 [Image is in the Public Domain]

That said, Joire was at least trying to do things the right way.  He was obsessed with evidence of an afterlife, and investigated numerous claims of séances, table-rapping and table-turning, mediumship, automatic writing, and spirit photography, and (again like the SPR) found that the vast majority of them were outright hoaxes.

It's the remaining ones that are interesting.

The article at Future and Cosmos focuses on a series of experiments Joire did with a self-proclaimed medium and four other people as participants/witnesses, where "unseen agents" were questioned and asked for details of their lives and deaths.  The "agents" responded by rapping on the table to spell out in painstaking fashion words and sentences, which were then recorded by Joire.  The gist of the claim is that the information the ghosts were providing was unavailable to anyone at the table, and was only verified as correct after the fact (some were never verified, but never disproven; none, Joire said, was researched and proven false).  You should read the blog post in its entirety, and I don't want to steal the author's thunder, but here is just one of many examples:

Question. Bertolf must be a Christian name. Have you any other name ?
Answer. Bertolf de Ghistelles.
Q. Were you French ?
A. Flemish.
Q, Will you tell us the name of the locality where you lived ?
A, Dunkerque.
Q. Have you been a long time in the Beyond ?
A. Yes.
Q. In what year did you die ?
A. In 1081.
Q. What were you ?
A, Husband of a Saint.
Q. Do you mean that your wife is honoured as a saint, that she has been canonised ?
A, Yes.
Q. What was her name ?
A, Godeleine de Wierfroy.  Can she forgive me ?
Q, You did her harm ?
A. Yes.
Q. You killed her perhaps ?
A, I had her strangled...
Q, Have you found any members of her family ?
A, Heinfried and his wife Ogine, her father and mother.  They have forgiven me.
Q. Is the festival of your wife celebrated anywhere ?
A. Yes.
Q. On what date ?
A, July 6th....
Q, Did you die in a tragic manner ?
A, No, in a monastery.  I remained there nine years.

Joire was able to verify that there was a woman, later canonized, named Godeleine (or Godelive or Godelieve) of Ghistelles, who was murdered by her husband Berthold [sic] and her body thrown down a well; the remorseful Berthold later became a monk.

The author of Future and Cosmos has the following to say about Joire's experiments and conclusions:

[This would require] some extremely elaborate and very hard-to-prepare fraud in which a medium learned and meticulously memorized very many details about deceased figures (some not famous), and then orally recited those details, only pretending to be entranced...  The total number of raps needed to spell out the details above (with one rap per letter) would have been many hundreds, occurring spread out over a long time.  We can imagine no medium manually producing so many hundreds of raps at a table where five people were seated, without being detected by the investigators.

The only other "narrow possibility" we have of Joire's experiments not being actual evidence of spirit survival, we're told, is if the entire thing was fraudulent; i.e., that Joire himself fabricated it all.

Okay, so what do we make of this?

First, I'll agree with the author that if it's a fraud, it's a sophisticated one.  But the problem is in the last sentence; "We can imagine no medium [accomplishing this] without being detected."  Humans are notoriously easy to fool -- consider how readily we fall for the conjuring illusions of a professional stage magician -- especially when we have a vested interest in believing that the thing we're being fooled about is true.  After all, most of us, myself included, would love it if there were an afterlife.  For me, though, I'd prefer that it not be the harps, haloes, and fields of flowers variety.  I'd be thrilled with something like Valhalla, where you get to spend eternity whooping it up with your friends, participating in daily debauchery involving riotous parties, quaffing tankards of mead, and lots of sex.  So despite my general dubious attitude toward claims of spirit survival, I'm not honestly hostile to the idea, and no one would be happier than me if I turned out to  be wrong.

The thing that bothers me with Joire's experiments is the quality of the evidence.  Joire was able to verify the details in a great many of the cases (and there were a lot of cases; his book is apparently 635 pages long), which means that the details on these people's lives were out there somewhere prior to the experiments being run.  The author of Future and Cosmos says that after reading his accounts we'd be "unlikely to suspect so serious a scholar of that type of chicanery," but unfortunately, there is no human who is above suspicion.  A quick google search for "scientific fraud" will turn up hundreds of examples, some of which had people fooled for years and were debunked more or less by accident.  Scientists, sad to say, are no less prone to the temptations to cheat than the rest of us are.  Most people are honest, and do their best to play fair; but you can't start from the assumption that because a person is a scientist, (s)he is incapable of fraud.

What we can rely on, though, are the methods of science.  The rigor of the scientific approach is set up to exclude the drawing of false conclusions, whether because of innocent error or deliberate falsification, and I don't see how the evidence provided by Joire meets the minimum standard we'd require in order to agree with his conclusions (and those of the author of Future and Cosmos).  I recognize that this means his spirit-rapping question-and-answer sessions fall into a catch-22 -- if the actual accounts of the deceased subjects' lives were already out there, it opens up the possibility of foreknowledge and cheating; but if no such accounts existed, there'd be no way to verify that what the "spirits" said was true.  This, however, is an inherent flaw of the experimental design -- one that makes its results fail to achieve any kind of scientific rigor.

Note, though, that I'm not saying that Joire was a dupe or a fraud, or that he didn't communicate with the disembodied spirit of Bertolf de Ghistelles and other folks.  There is the possibility that Joire's accounts are nothing less than the unvarnished truth, and if you're going to keep an open mind, you have to admit that there's no positive evidence of fraud on the part of Joire or the medium.

But as Carl Sagan said, extraordinary claims require extraordinary evidence.  Unless you're starting by assuming your conclusion, you'd need more than this to buy what Joire is saying.  So as far as the possibility of a fun-filled Valhalla waiting for me, I'm going to have to temper my enthusiasm and wait for better data.

*************************************

It's kind of sad that there are so many math-phobes in the world, because at its basis, there is something compelling and fascinating about the world of numbers.  Humans have been driven to quantify things for millennia -- probably beginning with the understandable desire to count goods and belongings -- but it very quickly became a source of curiosity to find out why numbers work as they do.

The history of mathematics and its impact on humanity is the subject of the brilliant book The Art of More: How Mathematics Created Civilization by Michael Brooks.  In it he looks at how our ancestors' discovery of how to measure and enumerate the world grew into a field of study that unlocked hidden realms of science -- leading Galileo to comment, with some awe, that "Mathematics is the language with which God wrote the universe."  Brooks's deft handling of this difficult and intimidating subject makes it uniquely accessible to the layperson -- so don't let your past experiences in math class dissuade you from reading this wonderful and eye-opening book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]



Tuesday, January 25, 2022

Eldritch rabbit holes

Between research for Skeptophilia, my choice of reading material, and natural curiosity, I go down some deep rabbit holes sometimes.

This latest plunge into the netherworld of knowledge happened because I decided to reread The Lurker at the Threshold by H. P. Lovecraft and August Derleth.  It's the umpteenth time I've read it, and although I'm well aware of its flaws (especially the overuse of words like "eldritch," the fact that every damn character in the story lives in an "ancient gambrel-roofed house," and the seemingly rushed/thinly-plotted final section), that book has some serious atmosphere.  I swear, I'll never see a stained-glass window again without thinking of the scene where the main character looks through the clear central pane of the crazy circular window in the library of the house where the story takes place -- and sees not the woods and stream lying outside, but a vista of an alien planet.

Near the end of the story, the scientist/historian Dr. Lapham is trying to convince his assistant that there's something supernatural going on, and goes through a bunch of examples from history of inexplicable occurrences.  I recognized one of them as being an actual event -- the disappearance of British diplomatic envoy Benjamin Bathurst in Perleberg, Germany in 1809 -- although the way it's described makes it sound way weirder than it actually was, and it's almost certain that Bathurst was simply robbed and murdered.  (This didn't stop me from giving the event a passing mention in my own novel, Sephirot.  Hey, if Lovecraft can get away with it, so can I.)

The fact that the Bathurst incident has at least a basis in reality made me wonder about a couple of the others Dr. Lapham mentions.  Several are references to other (fictional) Lovecraft stories, but I did wonder about his mention of sightings of mysterious undersea lights by the crews of two British ships, the light cruiser H. M. S. Caroline and the second-class cruiser H. M. S. Leander, in 1893.  So I did a bit of digging, and although the ships themselves were 100% real, I couldn't find any reference to odd sightings from either one.  

Anyhow, in The Lurker at the Threshold, the lights were supposedly the hallmark of the evil "Great Old One" Yog-Sothoth, who appeareth unto mankind as congeries of iridescent globes, so although I hath no idea what the fuck a "congery" is, I googled "real sightings of Yog-Sothoth," and that's when the bottom fell out of the rabbit hole.

The Invocation of Yog-Sothoth [Image licensed under the Creative Commons Demodus, Attribution-Noncommercial-Share Alike 3.0 License, Template:Other free]

This is how I ended up at a site called Lovecraftian Science, about which I can't for the life of me tell if the owner is serious.  Apparently the guy is a legitimate limnologist/ecologist, so it could well be that he's just having a bit of fun trying to apply the methods of science to the world of the Cthulhu Mythos, but damned if he doesn't seem entirely in earnest.

Amongst the entries I saw therein:
  • "Cryptobiosis in Elder Things: Drifting Through Interstellar Space" -- in which we find out that the "Elder Things" in Lovecraft's "At the Mountains of Madness" go into stasis when they're in outer space, and are propelled from one planet to another by dark energy.  We also read speculation that the members of the Elder Things have a similar protein structure to tardigrades, and that's how they manage to survive the trip from one planet to the next.
  • "Stephen Hawking's Ideas in a Lovecraftian Cosmos" -- wherein we learn that the titular musician in "The Music of Erich Zann" prevented an invasion of our universe by "extra-dimensional beings" by "generating micro-scale gravity waves of a very specific disturbance within space-time to link our universe with another."  Whatever that means.
  • "Lovecraftian Scientists: Astronomers from 'Beyond the Wall of Sleep'" -- musings on how the spirit of Joe Slater, main character in the short story mentioned in the title of the post, could have done battle with the evil entity residing near a star in the constellation of Perseus resulting in a spectacular nova observed in 1901 -- when the nova is 1,500 light years away, so the actual explosion happened 1,500 years ago.  "We do not know if the luminescent being that possessed Joe Slater could travel through time as easily as space so its existence was not limited to strictly linear time as it is with us," the author writes, apparently with a straight face.
  • "Lovecraft's 'Facts Concerning the Late Arthur Jermyn and His Family:' What of the Piltdown Man?" -- because there's nothing that strengthens an argument about the factual nature of a fictional story like drawing evidence from a blatant hoax.
  • "'The Dunwich Horror:' Meet the Whateleys" -- in which I found out way more than I wanted to know about the mechanics of Yog-Sothoth having sex with Lavinia Whateley, along with, I shit you not, Punnett squares for the offspring thereof.
I encourage you to peruse the website, because this is barely scratching the surface.  Whatever you can say about the guy's level of seriousness, there's no doubt that he's dedicated.

Being a writer, I've often joked about the FBI keeping a file on my google search history, but there are times I'm guessing that even the FBI would take the whole file and dump it in the trash and say, "Okay, never mind, this guy is a fucking loon."  I guess it's an occupational hazard of the combination of (1) being a speculative fiction writer, (2) owning a blog that frequently focuses on beliefs in weird stuff, and (3) having insatiable curiosity.  On the other hand, I'm not sure if it's disturbing or reassuring that there are people who go way further into the rabbit hole than I do; some of them, in fact, seem to have taken up permanent residence.

Anyhow, I'm going to try to go back to topics from science tomorrow.  I think one day of investigating eldritch giant interstellar tardigrades and what it'd be like to get laid by "congeries of iridescent globes" is enough to last me for a long time.

*************************************

It's kind of sad that there are so many math-phobes in the world, because at its basis, there is something compelling and fascinating about the world of numbers.  Humans have been driven to quantify things for millennia -- probably beginning with the understandable desire to count goods and belongings -- but it very quickly became a source of curiosity to find out why numbers work as they do.

The history of mathematics and its impact on humanity is the subject of the brilliant book The Art of More: How Mathematics Created Civilization by Michael Brooks.  In it he looks at how our ancestors' discovery of how to measure and enumerate the world grew into a field of study that unlocked hidden realms of science -- leading Galileo to comment, with some awe, that "Mathematics is the language with which God wrote the universe."  Brooks's deft handling of this difficult and intimidating subject makes it uniquely accessible to the layperson -- so don't let your past experiences in math class dissuade you from reading this wonderful and eye-opening book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]